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C22⋊C4×C22⋊D79 #23766219

order10112
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22⋊C4×C22⋊D79

Splittings

FittingC22×C22⋊C4×C79 ⋊ C2
SylowC79 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
FittingC22×C22⋊C4×C79C2
socle, cosocleC23×C79C24
prime radicalC23×C22⋊D79C2
hypercenterC22×C22⋊C4D79
hypocenterC79D4×C22⋊C4
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C22⋊C4

1252 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1610 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#34303589, #99×C22⋊D79, #34304397, …
maximal normal subgroup of#34303589, #99×C22⋊D79, #34304397, …
maximal quotient ofC22⋊C4×(C2×D79)⋊C4, C22⋊C4×C22⋊Dic79, C22⋊C4×Dic79⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 7329);