Finite Group Databasebeta

M16×Dic74 #18003549

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×Dic74

Splittings

SylowC37 ⋊ Q8×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D37
commutator, socleC22×C37C23×C4
FittingC4×M16×C37C2
prime radicalC23×C37C22×C4
cosocleC2×C4×C37C24
hypercenterC4×M16D37
hypocenterC37Q8×M16
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C4×M16

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 13463);