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C2×#19127457 #24907163

order10624
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#19127457

Splittings

SylowC83 ⋊ C2×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC2×C4C4×Dic83
commutatorC4×C83C2×C42
FrattiniC22×C4C22×D83
FittingC2×#117×C83C2
socleC22×C83#95
prime radicalC24×C83D4
cosocleC22×C4×C83C23
hypercenterC2×#117D83
hypocenterC83C2×H(3,ℤ/4)
LCSG ▷ C4×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×#117

404 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1684 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofH(3,ℤ/4)×Dic83, C4×#19127457, #35309572, …
maximal normal subgroup ofH(3,ℤ/4)×Dic83, C4×#19127457, #35309572, …
maximal quotient ofC2×#24905291, C2×#24905292, #35293802, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10624, 4210);