Finite Group Databasebeta

C2×#17988661 #22618613

order9344
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#17988661

Splittings

FittingC2×C22⋊C8×C73 ⋊ C2
SylowC73 ⋊ C2×#435

Subgroups

subgroupG/H
centerC22×C4C22×D73
commutatorC22×C73C23×C4
FrattiniC2×C4C23×D73
FittingC2×C22⋊C8×C73C2
socleC23×C73C22×C4
hypercenterC2×C22⋊C8D73
hypocenterC73C2×#435
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

564 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1496 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#32995213, #33084301, #33084312, …
maximal normal subgroup of#32995213, #33084301, #33084312, …
maximal quotient ofC2×#22608763, C2×#22608777, C2×#22608770, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 13192);