Finite Group Databasebeta

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C3×C7⋊(C11⋊#1042) #37528613

order23100
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC3×C52×C7×C11 ⋊ C4
derived, HallC52×C7×C11 ⋊ C3×C4
HallC3×C52×C11 ⋊ Dic7
HallC3×C52×C7 ⋊ Dic11
HallC52×C11 ⋊ C3×Dic7
HallC3×C7×C11 ⋊ #1042
HallC52×C7 ⋊ C3×Dic11
HallC7×C11 ⋊ C3×#1042
HallC3×C52 ⋊ Dic77
HallC3×C11 ⋊ C7⋊#1042
SylowC52 ⋊ C3×Dic77
HallC3×C7 ⋊ C11⋊#1042
SylowC11 ⋊ C3×C7⋊#1042
SylowC7 ⋊ C3×C11⋊#1042

Subgroups

subgroupG/H
center, hypercenterC3C7⋊(C11⋊#1042)
commutator, hypocenterC52×C7×C11C3×C4
FrattiniC1G
Fitting, socleC3×C52×C7×C11C4
prime radicalC3×C5×C7×D5×C11C2
cosocleC5×C7×D5×C11C2×C3
LCSG ▷ C52×C7×C11
UCSC1 ◁ C3

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

2319 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 424);