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M16×Dic178 #26029205

order11392
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×Dic178

Splittings

SylowC89 ⋊ Q8×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D89
commutator, socleC22×C89C23×C4
FittingC4×M16×C89C2
prime radicalC23×C89C22×C4
cosocleC2×C4×C89C24
hypercenterC4×M16D89
hypocenterC89Q8×M16
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C4×M16

388 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1810 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#36448762, #36448766, #36448776, …
maximal normal subgroup of#36448762, #36448766, #36448776, …
maximal quotient ofM16×C4⋊Dic89, M16×#13083553, #36553077, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 13463);