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C2×C4⋊C4×Dic89 #26022589

order11392
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4⋊C4×Dic89

Splittings

SylowC89 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC24C22×D89
commutatorC2×C89C22×C42
FrattiniC23C23×D89
FittingC22×C4⋊C4×C89C2
socle, prime radicalC24×C89C23
cosocleC23×C89C24
hypercenterC22×C4⋊C4D89
hypocenterC89C2×C4×C4⋊C4
LCSG ▷ C2×C89 ▷ C89
UCSC1 ◁ C24 ◁ C22×C4⋊C4

928 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#324×Dic89, #36444944, #36447087, …
maximal normal subgroup of#324×Dic89, #36444944, #36447087, …
maximal quotient ofC2×#95×Dic89, C4×C4⋊C4×Dic89, C2×#26018477, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 6847);