Finite Group Databasebeta

C4×#22575446 #46813434

order34432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC4×#22575446

Splittings

SylowC269 ⋊ C4×#126

Subgroups

subgroupG/H
centerC22×C4C22×D269
commutatorC22×C269C23×C4
FrattiniC23C23×D269
FittingC4×C22⋊C4×C269C2
socle, cosocleC23×C269C24
prime radicalC24×C269C23
hypercenterC4×C22⋊C4D269
hypocenterC269C4×#126
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

Conjugacy classes & character table

5416 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 7059);