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C4×C22⋊D383 #27133802

order12256
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×C22⋊D383

Splittings

FittingC22×C4×C383 ⋊ C2
SylowC383 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D383
commutatorC2×C383C22×C4
FrattiniC22C22×D383
FittingC22×C4×C383C2
socle, cosocleC22×C383C23
prime radicalC2×C22⋊D383C2
hypercenterC22×C4D383
hypocenterC383C4×D4
LCSG ▷ C2×C383 ▷ C383
UCSC1 ◁ C2×C4 ◁ C22×C4

94 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3076 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of(C22⋊D383)⋊C8, C8×C22⋊D383, #37588419, …
maximal normal subgroup of(C22⋊D383)⋊C8, C8×C22⋊D383, #37588419, …
maximal quotient ofC4×C22⋊Dic383, C4×(C2×D383)⋊C4, C4×Dic383⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12256, 107);