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Dic11×#63270 #26046437

order12012
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productDic11×#63270
unambiguous semidirect productC11⋊(C4×#63270)

Splittings

derived, HallC7×C11×C13 ⋊ C3×C4
HallC7×C13×Dic11 ⋊ C3
HallC11×#63270 ⋊ C4
HallC13×Dic11 ⋊ ΓL(1,𝔽8)
HallC7×Dic11 ⋊ C13⋊C3
HallC11×C13 ⋊ C4×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×Dic11
HallC7×C11 ⋊ C4×C13⋊C3
SylowC13 ⋊ ΓL(1,𝔽8)×Dic11
SylowC11 ⋊ C4×#63270
SylowC7 ⋊ C13⋊C3×Dic11

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D11×#63270
commutator, hypocenterC7×C11×C13C3×C4
Fitting, socle, cosocleC2×C7×C11×C13C2×C3
prime radicalC2×C11×#63270C2
LCSG ▷ C7×C11×C13
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

462 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×C13⋊C3×Dic11, C3×Dic11×#63270, Dic33×#63270
maximal normal subgroup ofΓL(1,𝔽8)×C13⋊C3×Dic11, C3×Dic11×#63270
maximal quotient ofDic11×#11717941, C3×Dic11×#63270, Dic33×#63270

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 27);