Finite Group Databasebeta

C2×#21454900 #30544952

order15616
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC2×#21454900

Splittings

SylowC61 ⋊ C2×#2982

Subgroups

subgroupG/H
centerC22×C4C23×D61
commutatorC2×C61C24×C8
FrattiniC2×C4C24×D61
FittingC22×C4×Q8×C61C2
socleC23×C61C23×C4
prime radicalC24×C61C22×C4
cosocleC2×C4×C61C25
hypercenterC22×C4×Q8D61
hypocenterC61C2×#2982
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

2234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2536 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1034507);