Finite Group Databasebeta

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C2×M16×Dic83 #24915870

order10624
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×M16×Dic83

Splittings

SylowC83 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC22×C4C22×D83
commutatorC2×C83C22×C42
FrattiniC2×C4C23×D83
FittingC22×M16×C83C2
socleC23×C83C22×C4
prime radicalC24×C83C2×C4
cosocleC2×C4×C83C24
hypercenterC22×M16D83
hypocenterC83C2×C4×M16
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C22×M16

656 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 ofH(3,ℤ/4)×Dic83, #338×Dic83, #339×Dic83, …
maximal normal subgroup ofH(3,ℤ/4)×Dic83, #338×Dic83, #339×Dic83, …
maximal quotient ofC2×M16×C83⋊C8, C2×#24905744, C2×#24905750, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10624, 12917);