Finite Group Databasebeta

#367×D127 #30640508

order16256
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#367×D127

Splittings

Fitting#367×C127 ⋊ C2
SylowC127 ⋊ C2×#367

Subgroups

subgroupG/H
centerC22D8×D127
commutatorC8×C127C22×C4
FrattiniC2×C8C22×D127
Fitting#367×C127C2
socleC22×C127C2×D8
prime radicalC22×D127D8
cosocleC2×C8×C127C23
hypercenter#367D127
hypocenterC127C2×#367
LCSG ▷ C8×C127 ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

168 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1430 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 6288);