Finite Group Databasebeta

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#117×Dic83 #24909806

order10624
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×Dic83

Splittings

SylowC83 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D83
commutatorC2×C83C22×C42
FrattiniC23C23×D83
FittingC2×#117×C83C2
socle, cosocleC23×C83C24
prime radicalC24×C83C23
hypercenterC2×#117D83
hypocenterC83C4×#117
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×#117

752 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 of#35297845, #35297849, H(3,ℤ/4)×Dic83, …
maximal normal subgroup of#35297845, #35297849, H(3,ℤ/4)×Dic83, …
maximal quotient of#376×Dic83, C4×C22⋊C4×Dic83, C4×C4⋊C4×Dic83, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10624, 6853);