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C2×M16×Dic89 #26028659

order11392
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×M16×Dic89

Splittings

SylowC89 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC22×C4C22×D89
commutatorC2×C89C22×C42
FrattiniC2×C4C23×D89
FittingC22×M16×C89C2
socleC23×C89C22×C4
prime radicalC24×C89C2×C4
cosocleC2×C4×C89C24
hypercenterC22×M16D89
hypocenterC89C2×C4×M16
LCSG ▷ C2×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C22×M16

656 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofH(3,ℤ/4)×Dic89, #338×Dic89, #339×Dic89, …
maximal normal subgroup ofH(3,ℤ/4)×Dic89, #338×Dic89, #339×Dic89, …
maximal quotient ofC2×M16×#10623494, C2×#26018533, C2×#26018539, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 12917);