Finite Group Databasebeta

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C2×#19098319 #23763100

order10112
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#19098319

Splittings

SylowC79 ⋊ C2×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC2×C4C4×Dic79
commutatorC4×C79C2×C42
FrattiniC22×C4C22×D79
FittingC2×#117×C79C2
socleC22×C79#95
prime radicalC24×C79D4
cosocleC22×C4×C79C23
hypercenterC2×#117D79
hypocenterC79C2×H(3,ℤ/4)
LCSG ▷ C4×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×#117

404 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1604 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofH(3,ℤ/4)×Dic79, C4×#19098319, #34193437, …
maximal normal subgroup ofH(3,ℤ/4)×Dic79, C4×#19098319, #34193437, …
maximal quotient ofC2×#23761228, C2×#23761229, #34177667, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 4210);