Finite Group Databasebeta

C2×#21447153 #29708041

order15616
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21447153

Splittings

SylowC61 ⋊ C2×#2058

Subgroups

subgroupG/H
centerC24C2×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#336C2
socle, prime radicalC24×C61C2×D4
hypercenterC2×#336D61
hypocenterC61C2×#2058
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15616

Conjugacy classes & character table

2464 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 197596);