Finite Group Databasebeta

M16×Dic367 #37554137

order23488
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productM16×Dic367

Splittings

SylowC367 ⋊ C4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D367
commutatorC2×C367C2×C42
FittingC2×M16×C367C2
socleC22×C367C22×C4
prime radicalC23×C367C2×C4
cosocleC2×C4×C367C23
hypercenterC2×M16D367
hypocenterC367C4×M16
LCSG ▷ C2×C367 ▷ C367
UCSC1 ◁ C2×C4 ◁ C2×M16

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11744

Conjugacy classes & character table

3700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 500);