Finite Group Databasebeta

C4×#14556617 #22618739

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

Aliases

direct productC4×#14556617

Splittings

FittingC2×C4×D4×C73 ⋊ C2
SylowC73 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D73
commutatorC4×C73C23×C4
FrattiniC2×C4C23×D73
FittingC2×C4×D4×C73C2
socleC22×C73C22×D4
hypercenterC2×C4×D4D73
hypocenterC73C4×AGL(1,ℤ/8)
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

548 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1484 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#32980605, #32980611, #32980619, …
maximal normal subgroup of#32980605, #32980611, #32980619, …
maximal quotient ofC8×#14556617, #33055567, #33055587, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 13318);