Finite Group Databasebeta

← Prev (#23765967) Next (#23765969) →

C4×#14579159 #23765968

order10112
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#14579159

Splittings

SylowC79 ⋊ C4×C4⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D79
commutatorC22×C79C23×C4
FrattiniC23C23×D79
FittingC2×C4×Q8×C79C2
socle, prime radical, cosocleC23×C79C24
hypercenterC2×C4×Q8D79
hypocenterC79C4×C4⋊Q8
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

588 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#34182916, #34182917, #34182919, …
maximal normal subgroup of#34182916, #34182917, #34182919, …
maximal quotient ofC4×#19098458, C4×#19098470, C4×#19098468, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 7078);