Finite Group Databasebeta

C8×#16864402 #46819842

order34432
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC8×#16864402

Splittings

FittingC2×C4×C8×C269 ⋊ C2
SylowC269 ⋊ C8×#41

Subgroups

subgroupG/H
centerC4×C8C2×D269
commutatorC2×C269C23×C8
FrattiniC2×C4C23×D269
FittingC2×C4×C8×C269C2
socleC22×C269C23×C4
prime radicalC2×#16864402C4
cosocleC2×C4×C269C24
hypercenterC2×C4×C8D269
hypocenterC269C8×#41
LCSG ▷ C2×C269 ▷ C269
UCSC1 ◁ C4×C8 ◁ C2×C4×C8

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

Conjugacy classes & character table

8656 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 13467);