Finite Group Databasebeta

M16×#11745671 #28560129

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×#11745671

Splittings

FittingQ8×M16×C59 ⋊ C2
SylowC59 ⋊ M16×SD16

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingQ8×M16×C59C2
socleC22×C59C2×C4×D4
prime radicalC22×D236C2×C4
cosocleC42×C59C24
hypercenterQ8×M16D59
hypocenterC59M16×SD16
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ Q8×M16

716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1520 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 141008);