Finite Group Databasebeta

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C7×Dic305⋊C3 #38784976

order25620
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic305⋊C3
unambiguous semidirect productDic305⋊(C3×C7)

Splittings

derived, HallC5×C61 ⋊ C3×C4×C7
HallC7×Dic305 ⋊ C3
HallC5×C7×C61⋊C3 ⋊ C4
HallC5×C7×C61 ⋊ C3×C4
HallC7×C61⋊C3 ⋊ Dic5
HallDic305 ⋊ C3×C7
HallC5×C61⋊C3 ⋊ C4×C7
HallC7×C61 ⋊ C3×Dic5
HallC61⋊C3 ⋊ C7×Dic5
SylowC61 ⋊ C3×C7×Dic5
HallC5×C7 ⋊ Dic61⋊C3
SylowC5 ⋊ C7×Dic61⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C7C5⋊(D61⋊C3)
commutator, hypocenterC5×C61C3×C4×C7
FrattiniC2C7×C5⋊(D61⋊C3)
Fitting, socleC2×C5×C7×C61C2×C3
prime radicalC2×C5×C7×C61⋊C3C2
cosocleC2×C5×C61C2×C3×C7
LCSG ▷ C5×C61
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8540

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25620, 49);