Finite Group Databasebeta

C2×#17985829 #22590132

order9088
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#17985829

Splittings

SylowC71 ⋊ C2×#368

Subgroups

subgroupG/H
centerC2×C4D568
commutatorC8×C71C22×C4
FrattiniC2×C8C22×D71
FittingC22×C16×C71C2
socleC22×C71#107
hypercenterC22×C16D71
hypocenterC71C2×#368
LCSG ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2284 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#31885154, #31885155, #31885156, …
maximal normal subgroup of#31885154, #31885155, #31885156, …
maximal quotient ofC2×#22586412, C2×#22586414, #31909037, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9088, 6302);