Finite Group Databasebeta

C4×Dic584 #22611791

order9344
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic584

Splittings

SylowC73 ⋊ C4×Q32

Subgroups

subgroupG/H
centerC2×C4D584
commutatorC8×C73C22×C4
FrattiniC2×C8C22×D73
FittingC4×C16×C73C2
socleC22×C73C2×D8
hypercenterC4×C16D73
hypocenterC73C4×Q32
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×C16

150 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#32973436, #32973438, #32973442, …
maximal normal subgroup of#32973436, #32973438, #32973442, …
maximal quotient ofC8×Dic584, #32997902, #32997976, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 6370);