Finite Group Databasebeta

C2×C4×#14519757 #29838465

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×C4×#14519757

Splittings

FittingC2×C4×C4⋊C4×C61 ⋊ C2
SylowC61 ⋊ C2×C4×C22⋊Q8

Subgroups

subgroupG/H
centerC23×C4C22×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C4×C4⋊C4×C61C2
socleC24×C61C24
prime radicalC24×D61C23
cosocleC23×C61C25
hypercenterC2×C4×C4⋊C4D61
hypocenterC61C2×C4×C22⋊Q8
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

3854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 328020);