Finite Group Databasebeta

C4⋊C4×D488 #29698408

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C4×D488

Splittings

FittingC8×C4⋊C4×C61 ⋊ C2
SylowC61 ⋊ C4⋊C4×D8

Subgroups

subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC8×C4⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC22×D488C22
cosocleC22×C4×C61C24
hypercenterC8×C4⋊C4D61
hypocenterC61C4⋊C4×D8
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ C8×C4⋊C4

1134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 187963);