Finite Group Databasebeta

C2×#21445537 #29677415

order15616
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#21445537

Splittings

FittingC2×C61×#340 ⋊ C2
SylowC61 ⋊ C2×#1736

Subgroups

subgroupG/H
centerC24D4×D61
commutatorC4×C61C22×C42
FrattiniC22×C4C23×D61
FittingC2×C61×#340C2
socleC24×C61C2×D4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenterC2×#340D61
hypocenterC61C2×#1736
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

2574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 166970);