Finite Group Databasebeta

#367×D109 #28364810

order13952
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#367×D109

Splittings

Fitting#367×C109 ⋊ C2
SylowC109 ⋊ C2×#367

Subgroups

subgroupG/H
centerC22D8×D109
commutatorC8×C109C22×C4
FrattiniC2×C8C22×D109
Fitting#367×C109C2
socleC22×C109C2×D8
prime radicalC22×D109D8
cosocleC2×C8×C109C23
hypercenter#367D109
hypocenterC109C2×#367
LCSG ▷ C8×C109 ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 6288);