Finite Group Databasebeta

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C4×#16839492 #29570613

order15616
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#16839492

Splittings

SylowC61 ⋊ C4×Q8⋊C8

Subgroups

subgroupG/H
centerC2×C42C22⋊D61
commutatorC4×C61C2×C4×C8
FrattiniC2×C42C22×D61
FittingC4×C4⋊C8×C61C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenterC4×C4⋊C8D61
hypocenterC61C4×Q8⋊C8
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C42 ◁ C43 ◁ C4×C4⋊C8

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15616

Conjugacy classes & character table

2512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 60168);