Finite Group Databasebeta

C2×#21448171 #29838217

order15616
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#21448171

Splittings

FittingC2×C4×C22⋊C4×C61 ⋊ C2
SylowC61 ⋊ C2×#2273

Subgroups

subgroupG/H
centerC24C23×D61
commutatorC2×C61C23×C42
FrattiniC23C24×D61
FittingC2×C4×C22⋊C4×C61C2
socleC24×C61C24
prime radicalC25×D61C22
cosocleC23×C61C25
hypercenterC2×C4×C22⋊C4D61
hypocenterC61C2×#2273
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

5790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

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, 327772);