Finite Group Databasebeta

C2×#17985827 #22590120

order9088
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#17985827

Splittings

SylowC71 ⋊ C2×#367

Subgroups

subgroupG/H
centerC23D568
commutatorC8×C71C22×C4
FrattiniC2×C8C22×D71
FittingC22×C16×C71C2
socleC23×C71D8
hypercenterC22×C16D71
hypocenterC71C2×#367
LCSG ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

168 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#31885160, #31885161, #31885166, …
maximal normal subgroup of#31885160, #31885161, #31885166, …
maximal quotient ofC2×#22586414, #31909097, #31909137, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9088, 6290);