Finite Group Databasebeta

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C4×#15667977 #26022601

order11392
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#15667977

Splittings

SylowC89 ⋊ C42×Q8

Subgroups

subgroupG/H
centerC22×C4C22×D89
commutatorC2×C89C22×C42
FrattiniC23C23×D89
FittingC4×C4⋊C4×C89C2
socle, prime radical, cosocleC23×C89C24
hypercenterC4×C4⋊C4D89
hypocenterC89C42×Q8
LCSG ▷ C2×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

684 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#36445024, #36445034, #36445044, …
maximal normal subgroup of#36445024, #36445034, #36445044, …
maximal quotient ofC4×#19151449, C4×C4⋊C4×Dic89, #36475600, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 6859);