Finite Group Databasebeta

C2×#21460717 #30597186

order15616
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21460717

Splittings

SylowC61 ⋊ C2×#1303

Subgroups

subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×#95×C61C4
socleC23×C61#95
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#95#6923
hypocenterC61C2×#1303
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1086741);