Finite Group Databasebeta

← Prev (#30614249) Next (#30614251) →

C4⋊C4×#11758213 #30614250

order15616
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4⋊C4×#11758213

Splittings

SylowC61 ⋊ C4⋊C4×M16

Subgroups

subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C22×C42
FittingC4×C4⋊C4×C61C4
socleC23×C61C23×C4
prime radicalC23×D61C22×C4
cosocleC22×Dic61C24
hypercenterC4×C4⋊C4#6923
hypocenterC61C4⋊C4×M16
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4

1242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1103805);