Finite Group Databasebeta

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C4×#14579071 #23763084

order10112
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C2×C42

Aliases

direct productC4×#14579071

Splittings

SylowC79 ⋊ C4×#97

Subgroups

subgroupG/H
centerC2×C42C2×D79
commutatorC2×C79C43
FrattiniC22×C4C22×D79
FittingC2×C4×C8×C79C2
socle, prime radicalC23×C79C22×C4
cosocleC22×C4×C79C23
hypercenterC2×C4×C8D79
hypocenterC79C4×#97
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

360 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2576 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#34175126, C8×#14579071, #34177621, …
maximal normal subgroup of#34175126, C8×#14579071, #34177621, …
maximal quotient ofC4×#19098284, C4×#19098285, C8×#14579071, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 4194);