Finite Group Databasebeta

← Prev (#26023153) Next (#26023155) →

D4×C4⋊Dic89 #26023154

order11392
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×C4⋊Dic89

Splittings

SylowC89 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D89
commutatorC22×C89C23×C4
FittingC2×C4×D4×C89C2
socle, cosocleC23×C89C24
prime radicalC22×D4×C89C22
hypercenterC2×C4×D4D89
hypocenterC89D4×C4⋊C4
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C4×D4

776 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#36448586, #36448590, #36448614, …
maximal normal subgroup of#36448586, #36448590, #36448614, …
maximal quotient ofC22⋊C4×C4⋊Dic89, C4⋊C4×C4⋊Dic89, D4×#15667919, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 7412);