Finite Group Databasebeta

C4×#10625072 #15681817

order2944
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#10625072

Splittings

FittingC2×C4×C8×C23 ⋊ C2
SylowC23 ⋊ C4×#131

Subgroups

subgroupG/H
centerC4×C8C2×D23
commutatorC2×C23C22×C42
FrattiniC2×C4C23×D23
FittingC2×C4×C8×C23C2
socleC22×C23C23×C4
prime radicalC2×#67288C22
cosocleC2×C4×C23C24
hypercenterC2×C4×C8D23
hypocenterC23C4×#131
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C4×C8 ◁ C2×C4×C8

572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 12930);