Finite Group Databasebeta

C2×C4×#14519722 #29833282

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C4×#14519722

Splittings

FittingC2×C4×C16×C61 ⋊ C2
SylowC61 ⋊ C2×C4×SD32

Subgroups

subgroupG/H
centerC22×C4D488
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC2×C4×C16×C61C2
socleC23×C61C2×D8
prime radicalC22×D488C22
cosocleC2×C8×C61C24
hypercenterC2×C4×C16D61
hypocenterC61C2×C4×SD32
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×C16

742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

3928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 322837);