Finite Group Databasebeta

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D4×(C2×D83)⋊C4 #24910280

order10624
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD4×(C2×D83)⋊C4

Splittings

FittingC2×C4×D4×C83 ⋊ C2
SylowC83 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D83
commutatorC22×C83C23×C4
FittingC2×C4×D4×C83C2
socle, cosocleC23×C83C24
prime radicalC22×D4×D83C2
hypercenterC2×C4×D4D83
hypocenterC83D4×C22⋊C4
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4

1252 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1690 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#35420109, #35420110, #35420117, …
maximal normal subgroup of#35420109, #35420110, #35420117, …
maximal quotient ofC22⋊C4×(C2×D83)⋊C4, C4⋊C4×(C2×D83)⋊C4, D4×C83⋊#95, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10624, 7327);