Finite Group Databasebeta

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#117×Dic71 #22590683

order9088
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×Dic71

Splittings

SylowC71 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D71
commutatorC2×C71C22×C42
FrattiniC23C23×D71
FittingC2×#117×C71C2
socleC23×C71C24
hypercenterC2×#117D71
hypocenterC71C4×#117
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×#117

752 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#31890893, #31890897, H(3,ℤ/4)×Dic71, …
maximal normal subgroup of#31890893, #31890897, H(3,ℤ/4)×Dic71, …
maximal quotient of#376×Dic71, C4×C22⋊C4×Dic71, C4×C4⋊C4×Dic71, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9088, 6853);