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C4×C22⋊D379 #27131292

order12128
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×C22⋊D379

Splittings

FittingC22×C4×C379 ⋊ C2
SylowC379 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D379
commutatorC2×C379C22×C4
FrattiniC22C22×D379
FittingC22×C4×C379C2
socle, cosocleC22×C379C23
prime radicalC2×C22⋊D379C2
hypercenterC22×C4D379
hypocenterC379C4×D4
LCSG ▷ C2×C379 ▷ C379
UCSC1 ◁ C2×C4 ◁ C22×C4

94 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3044 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of(C22⋊D379)⋊C8, C8×C22⋊D379, #37565312, …
maximal normal subgroup of(C22⋊D379)⋊C8, C8×C22⋊D379, #37565312, …
maximal quotient ofC4×C22⋊Dic379, C4×(C2×D379)⋊C4, C4×Dic379⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12128, 107);