Finite Group Databasebeta

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C4×#16812108 #28339031

order13696
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#16812108

Splittings

SylowC107 ⋊ C4×C4⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D107
commutatorC22×C107C23×C4
FrattiniC23C23×D107
FittingC4×C4⋊C4×C107C2
socle, prime radical, cosocleC23×C107C24
hypercenterC4×C4⋊C4D107
hypocenterC107C4×C4⋊Q8
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13696

Conjugacy classes & character table

2176 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 7080);