Finite Group Databasebeta

M16×Dic382 #37581473

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×Dic382

Splittings

SylowC191 ⋊ Q8×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D191
commutator, socleC22×C191C23×C4
FittingC4×M16×C191C2
prime radicalC23×C191C22×C4
cosocleC2×C4×C191C24
hypercenterC4×M16D191
hypocenterC191Q8×M16
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ C4×M16

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

3850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 13463);