Finite Group Databasebeta

C2×#21445820 #29679461

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#21445820

Splittings

FittingC22×C4⋊C8×C61 ⋊ C2
SylowC61 ⋊ C2×#1802

Subgroups

subgroupG/H
centerC24C2×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×C4⋊C8×C61C2
socleC24×C61C2×D4
prime radicalC23×D244C22
cosocleC22×C4×C61C24
hypercenterC22×C4⋊C8D61
hypocenterC61C2×#1802
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊C8

2030 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2476 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 169016);