Finite Group Databasebeta

C22×Dic584 #22623044

order9344
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic584

Splittings

SylowC73 ⋊ C22×Q32

Subgroups

subgroupG/H
centerC23D584
commutatorC8×C73C24
FrattiniC8C23×D73
FittingC22×C16×C73C2
socleC23×C73D8
hypercenterC22×C16D73
hypocenterC73C22×Q32
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

360 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2348 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#33003061, #33003063, #33003096, …
maximal normal subgroup of#33003061, #33003063, #33003096, …
maximal quotient ofC22×#17988392, C22×#17988413, C2×C4×Dic584, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 17623);