Finite Group Databasebeta

← Prev (#23765934) Next (#23765936) →

C4×#14579140 #23765935

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

Aliases

direct productC4×#14579140

Splittings

SylowC79 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D79
commutatorC22×C79C23×C4
FrattiniC23C23×D79
FittingC22×C42×C79C2
socle, cosocleC23×C79C24
prime radicalC24×C79C23
hypercenterC22×C42D79
hypocenterC79C4×C22⋊Q8
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C22×C42

656 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2552 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#34176231, #34176234, #34176304, …
maximal normal subgroup of#34176231, #34176234, #34176304, …
maximal quotient ofC4×#19098436, C4×#19098447, C4×#19098461, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 7045);