Finite Group Databasebeta

C2×#21444123 #29645720

order15616
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C8

Aliases

direct productC2×#21444123

Splittings

FittingC2×C61×#322 ⋊ C2
SylowC61 ⋊ C2×#1455

Subgroups

subgroupG/H
centerC2×C42C22×D61
commutatorC22×C61C22×C42
FrattiniC42C23×D61
FittingC2×C61×#322C2
socleC23×C61C2×C42
prime radicalC23×D61C42
cosocleC42×C61C24
hypercenterC2×#322D61
hypocenterC61C2×#1455
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C42 ◁ C2×#322

994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 135275);