Finite Group Databasebeta

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C4⋊C4×Dic30 #14327219

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×Dic30

Splittings

HallC3×C5 ⋊ Q8×C4⋊C4
SylowC5 ⋊ C4⋊C4×Dic6
SylowC3 ⋊ C4⋊C4×Dic10

Subgroups

subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C4×C5×C4⋊C4C2
socle, prime radical, cosocleC23×C3×C5C24
hypercenterC4×C4⋊C4D15
hypocenterC3×C5Q8×C4⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C4×C4⋊C4

1136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 52917);