Finite Group Databasebeta

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C7×C11⋊#64470 #37528364

order23100
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11⋊#64470
unambiguous semidirect productC11⋊(C7×#64470)

Splittings

derived, HallC11×C52⋊C3 ⋊ C4×C7
HallC7×C11×C52⋊C3 ⋊ C4
HallC52×C7×C11 ⋊ Dic3
HallC7×C52⋊C3 ⋊ Dic11
HallC52×C11 ⋊ C7×Dic3
HallC52×C7 ⋊ Dic33
HallC7×C11 ⋊ #64470
HallC52⋊C3 ⋊ C7×Dic11
SylowC52 ⋊ C7×Dic33
SylowC11 ⋊ C7×#64470

Subgroups

subgroupG/H
center, hypercenterC2×C7C11⋊#3874
commutator, hypocenterC11×C52⋊C3C4×C7
FrattiniC2C7×C11⋊#3874
Fitting, socleC2×C52×C7×C11D3
prime radicalC2×C7×C11×C52⋊C3C2
cosocleC2×C11×C52⋊C3C2×C7
LCSG ▷ C11×C52⋊C3
UCSC1 ◁ C2×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 175);