Finite Group Databasebeta

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C4×#14579138 #23765931

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

Aliases

direct productC4×#14579138

Splittings

SylowC79 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D79
commutatorC22×C79C23×C4
FrattiniC23C23×D79
FittingC4×C22⋊C4×C79C2
socle, cosocleC23×C79C24
prime radicalC24×C79C23
hypercenterC4×C22⋊C4D79
hypocenterC79C4×C22⋊Q8
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

656 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 ofC8×#14579138, #34295680, #34295690, …
maximal normal subgroup ofC8×#14579138, #34295680, #34295690, …
maximal quotient ofC4×#19098438, C4×#19098435, C4×#19098450, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 7041);