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C11×C7⋊#64480 #37528485

order23100
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C5

Aliases

direct productC11×C7⋊#64480
unambiguous semidirect productC7⋊(C11×#64480)

Splittings

Fitting, socle, HallC52×C7×C11 ⋊ Dic3
derived, HallC7×C52⋊C3 ⋊ C4×C11
HallC7×C11×C52⋊C3 ⋊ C4
HallC11×C52⋊C3 ⋊ Dic7
HallC52×C11 ⋊ Dic21
HallC52×C7 ⋊ C11×Dic3
HallC7×C11 ⋊ #64480
HallC52⋊C3 ⋊ C11×Dic7
SylowC52 ⋊ C11×Dic21
SylowC7 ⋊ C11×#64480

Subgroups

subgroupG/H
center, hypercenterC11C7⋊#64480
commutator, hypocenterC7×C52⋊C3C4×C11
FrattiniC1G
Fitting, socleC52×C7×C11Dic3
prime radicalC7×C11×(C5⋊D5)⋊C3C2
cosocleC7×(C5⋊D5)⋊C3C2×C11
LCSG ▷ C7×C52⋊C3
UCSC1 ◁ C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1155

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 296);