Finite Group Databasebeta

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C11×C3⋊(C7⋊#1042) #37528672

order23100
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊(C7⋊#1042)
unambiguous semidirect productC3⋊(C11×C7⋊#1042)
unambiguous semidirect productC7⋊(C11×C3⋊#1042)

Splittings

Fitting, socle, HallC3×C52×C7×C11 ⋊ C4
derived, HallC3×C52×C7 ⋊ C4×C11
HallC52×C7×C11 ⋊ Dic3
HallC3×C52×C11 ⋊ Dic7
HallC52×C11 ⋊ Dic21
HallC3×C7×C11 ⋊ #1042
HallC52×C7 ⋊ C11×Dic3
HallC7×C11 ⋊ C3⋊#1042
HallC3×C52 ⋊ C11×Dic7
HallC3×C11 ⋊ C7⋊#1042
SylowC52 ⋊ C11×Dic21
HallC3×C7 ⋊ C11×#1042
SylowC7 ⋊ C11×C3⋊#1042
SylowC3 ⋊ C11×C7⋊#1042

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C7⋊#1042)
commutator, hypocenterC3×C52×C7C4×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C4
prime radicalC3×C5×C7×D5×C11C2
cosocleC3×C5×C7×D5C2×C11
LCSG ▷ C3×C52×C7
UCSC1 ◁ C11

104 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

2343 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 483);