Finite Group Databasebeta

C2×#21461084 #30610041

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

Aliases

direct productC2×#21461084

Splittings

SylowC61 ⋊ C2×#1468

Subgroups

subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
Fitting, prime radicalC23×D4×C61C4
socleC23×C61C2×C22⋊C4
cosocleC22×Dic61C24
hypercenterC23×D4#6923
hypocenterC61C2×#1468
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C25 ◁ C23×D4

1490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1099596);