Finite Group Databasebeta

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C11×Dic273 #26046428

order12012
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic273
unambiguous semidirect productC3⋊(C11×Dic91)
unambiguous semidirect productC7⋊(C11×Dic39)

Splittings

derived, HallC3×C7×C13 ⋊ C4×C11
HallC3×C7×C11×C13 ⋊ C4
HallC7×C11×C13 ⋊ Dic3
HallC3×C11×C13 ⋊ Dic7
HallC3×C7×C11 ⋊ Dic13
HallC11×C13 ⋊ Dic21
HallC7×C13 ⋊ C11×Dic3
HallC7×C11 ⋊ Dic39
HallC3×C13 ⋊ C11×Dic7
HallC3×C11 ⋊ Dic91
HallC3×C7 ⋊ C11×Dic13
SylowC13 ⋊ C11×Dic21
SylowC7 ⋊ C11×Dic39
SylowC3 ⋊ C11×Dic91

Subgroups

subgroupG/H
center, hypercenterC2×C11D273
commutator, hypocenterC3×C7×C13C4×C11
FrattiniC2C11×D273
Fitting, socle, prime radicalC2×C3×C7×C11×C13C2
cosocleC2×C3×C7×C13C2×C11
LCSG ▷ C3×C7×C13
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3036 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×Dic819, C11×C3⋊#11763964, C11×C3⋊#11763963, …
maximal normal subgroup ofC11×C3⋊#11763964, C11×C3⋊#11763963, C11×C3⋊(ΓL(1,𝔽8)⋊Dic13), …
maximal quotient ofC11×Dic819, C11×C3⋊Dic273, C3×C11×Dic273

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 18);