Finite Group Databasebeta

C2×#21462684 #30625738

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

Aliases

direct productC2×#21462684

Splittings

SylowC61 ⋊ C2×#2975

Subgroups

subgroupG/H
centerC23C23×#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C23×C4
prime radicalC23×D244C4
cosocleC2×Dic61C25
hypercenterC22×C4⋊C4#6923
hypocenterC61C2×#2975
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4⋊C4

2586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1115293);