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#117×Dic89 #26022595

order11392
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×Dic89

Splittings

SylowC89 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D89
commutatorC2×C89C22×C42
FrattiniC23C23×D89
FittingC2×#117×C89C2
socle, cosocleC23×C89C24
prime radicalC24×C89C23
hypercenterC2×#117D89
hypocenterC89C4×#117
LCSG ▷ C2×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C2×#117

752 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#36447869, #36447873, H(3,ℤ/4)×Dic89, …
maximal normal subgroup of#36447869, #36447873, H(3,ℤ/4)×Dic89, …
maximal quotient of#376×Dic89, C4×C22⋊C4×Dic89, C4×C4⋊C4×Dic89, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 6853);