Finite Group Databasebeta

C2×#21462146 #30624077

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

Aliases

direct productC2×#21462146

Splittings

SylowC61 ⋊ C2×#2148

Subgroups

subgroupG/H
centerC2×C4#14519839
commutatorC8×C61C23×C4
FrattiniC8C23×#6923
FittingC2×#135×C61C4
socleC22×C61C2×#102
prime radicalC2×#135×D61C2
cosocleC8×D61C24
hypercenterC2×#135#6923
hypocenterC61C2×#2148
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#135

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1113632);