Finite Group Databasebeta

C2×C4×#14519739 #29838203

order15616
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×C4×#14519739

Splittings

FittingC2×C4×C4⋊C4×C61 ⋊ C2
SylowC61 ⋊ C2×C42×D4

Subgroups

subgroupG/H
centerC23×C4C22×D61
commutatorC2×C61C23×C42
FrattiniC23C24×D61
FittingC2×C4×C4⋊C4×C61C2
socleC24×C61C24
prime radicalC23×D244C22
cosocleC23×C61C25
hypercenterC2×C4×C4⋊C4D61
hypocenterC61C2×C42×D4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

5694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 327758);