Finite Group Databasebeta

← Prev (#24909806) Next (#24909808) →

C4×(C22⋊D83)⋊C4 #24909807

order10624
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×(C22⋊D83)⋊C4

Splittings

FittingC4×C22⋊C4×C83 ⋊ C2
SylowC83 ⋊ C42×D4

Subgroups

subgroupG/H
centerC22×C4C22×D83
commutatorC2×C83C22×C42
FrattiniC23C23×D83
FittingC4×C22⋊C4×C83C2
socle, cosocleC23×C83C24
prime radicalC22×C22⋊D83C22
hypercenterC4×C22⋊C4D83
hypocenterC83C42×D4
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

924 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1720 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC8×(C22⋊D83)⋊C4, #35402747, #35402752, …
maximal normal subgroup ofC8×(C22⋊D83)⋊C4, #35402747, #35402752, …
maximal quotient ofC4×#19127548, C4×C22⋊C4×Dic83, C4×#19127552, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10624, 6854);