Finite Group Databasebeta

#367×D269 #46812663

order34432
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#367×D269

Splittings

Fitting#367×C269 ⋊ C2
SylowC269 ⋊ C2×#367

Subgroups

subgroupG/H
centerC22D8×D269
commutatorC8×C269C22×C4
FrattiniC2×C8C22×D269
Fitting#367×C269C2
socleC22×C269C2×D8
prime radicalC22×D269D8
cosocleC2×C8×C269C23
hypercenter#367D269
hypocenterC269C2×#367
LCSG ▷ C8×C269 ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

Conjugacy classes & character table

2992 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 6288);