Finite Group Databasebeta

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C4×#15668011 #26022822

order11392
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#15668011

Splittings

SylowC89 ⋊ C4×C4⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D89
commutatorC22×C89C23×C4
FrattiniC23C23×D89
FittingC4×C4⋊C4×C89C2
socle, prime radical, cosocleC23×C89C24
hypercenterC4×C4⋊C4D89
hypocenterC89C4×C4⋊Q8
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

588 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1816 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#36454407, #36454411, #36454425, …
maximal normal subgroup of#36454407, #36454411, #36454425, …
maximal quotient ofC4×#19151497, C4×#19151495, C4×#19151494, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 7080);