Finite Group Databasebeta

C2×#21462114 #30624007

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

Aliases

direct productC2×#21462114

Splittings

SylowC61 ⋊ C2×#2133

Subgroups

subgroupG/H
centerC22C2×#14519835
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
Fitting, prime radicalC22×#41×C61C4
socleC22×C61C2×#99
cosocleC2×Dic122C24
hypercenterC22×#41#6923
hypocenterC61C2×#2133
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C22×#41

1198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1113562);