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Dic11×C7⋊(C52⋊C3) #37528378

order23100
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C5

Aliases

direct productDic11×C7⋊(C52⋊C3)
unambiguous semidirect productC11⋊(C4×C7⋊(C52⋊C3))
unambiguous semidirect product(C7×Dic11)⋊(C52⋊C3)
unambiguous semidirect product(C52×Dic11)⋊ΓL(1,𝔽8)

Splittings

derived, HallC52×C7×C11 ⋊ C3×C4
HallC52×C7×Dic11 ⋊ C3
HallC11×C7⋊(C52⋊C3) ⋊ C4
HallC52×Dic11 ⋊ ΓL(1,𝔽8)
HallC7×Dic11 ⋊ C52⋊C3
HallC52×C11 ⋊ C4×ΓL(1,𝔽8)
HallC52×C7 ⋊ C3×Dic11
HallC7×C11 ⋊ C4×C52⋊C3
SylowC52 ⋊ ΓL(1,𝔽8)×Dic11
SylowC11 ⋊ C4×C7⋊(C52⋊C3)
SylowC7 ⋊ Dic11×C52⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D11×C7⋊(C52⋊C3)
commutator, hypocenterC52×C7×C11C3×C4
Fitting, socle, cosocleC2×C52×C7×C11C2×C3
prime radicalC2×C11×C7⋊(C52⋊C3)C2
LCSG ▷ C52×C7×C11
UCSC1 ◁ C2

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 189);