Finite Group Databasebeta

#386×D269 #46813299

order34432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct product#386×D269

Splittings

Fitting#386×C269 ⋊ C2
SylowC269 ⋊ C2×#386

Subgroups

subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#386×C269C2
socle, cosocleC23×C269C24
prime radicalC22×D4×D269C2
hypercenter#386D269
hypocenterC269C2×#386
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #386

1576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8608

Conjugacy classes & character table

3808 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 6924);