Finite Group Databasebeta

M16×Dic394 #38751665

order25216
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×Dic394

Splittings

SylowC197 ⋊ Q8×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D197
commutator, socleC22×C197C23×C4
FittingC4×M16×C197C2
prime radicalC23×C197C22×C4
cosocleC2×C4×C197C24
hypercenterC4×M16D197
hypocenterC197Q8×M16
LCSG ▷ C22×C197 ▷ C197
UCSC1 ◁ C2×C4 ◁ C4×M16

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12608

Conjugacy classes & character table

3970 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 13463);