Finite Group Databasebeta

C2×#21454283 #30543487

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#21454283

Splittings

SylowC61 ⋊ C2×#2884

Subgroups

subgroupG/H
centerC22C22×C22⋊Dic61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
Fitting, prime radicalC22×2−1+4×C61C2
socleC22×C61C22×C22⋊C4
cosocleC23×C61C25
hypercenterC22×2−1+4D61
hypocenterC61C2×#2884
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×Q8 ◁ C22×2−1+4

4818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1033042);