Finite Group Databasebeta

C2×#21454820 #30544494

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21454820

Splittings

FittingC2×C8×D4×C61 ⋊ C2
SylowC61 ⋊ C2×#2969

Subgroups

subgroupG/H
centerC22×C4C23×D61
commutatorC22×C61C24×C4
FrattiniC2×C4C24×D61
FittingC2×C8×D4×C61C2
socleC23×C61C23×C4
prime radicalC2×#14519748C4
cosocleC2×C4×C61C25
hypercenterC2×C8×D4D61
hypocenterC61C2×#2969
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C8×D4

2014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1034049);