Finite Group Databasebeta

C2×#21444165 #29645955

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21444165

Splittings

FittingC22×C22⋊C8×C61 ⋊ C2
SylowC61 ⋊ C2×#1468

Subgroups

subgroupG/H
centerC23C2×#11758198
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×C22⋊C8×C61C2
socleC23×C61C2×C22⋊C4
prime radicalC23×C22⋊D61C4
cosocleC22×C4×C61C24
hypercenterC22×C22⋊C8D61
hypocenterC61C2×#1468
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊C8

1490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2464 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 135510);