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C7×Dic7×ΓL(1,𝔽32) #44477131

order30380
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic7×ΓL(1,𝔽32)
unambiguous semidirect productC7⋊(C4×C7×ΓL(1,𝔽32))
unambiguous semidirect product(Dic7×C31)⋊(C5×C7)
unambiguous semidirect product(C7×Dic7×C31)⋊C5

Splittings

derivedC7×C31 ⋊ C4×C5×C7
HallC72×ΓL(1,𝔽32) ⋊ C4
HallC7×Dic7×C31 ⋊ C5
HallC72×C31 ⋊ C4×C5
SylowC72 ⋊ C4×ΓL(1,𝔽32)
SylowC31 ⋊ C5×C7×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C7D7×ΓL(1,𝔽32)
commutator, hypocenterC7×C31C4×C5×C7
FrattiniC2C7×D7×ΓL(1,𝔽32)
Fitting, socleC2×C72×C31C2×C5
prime radicalC2×C72×ΓL(1,𝔽32)C2
cosocleC2×C7×C31C2×C5×C7
LCSG ▷ C7×C31
UCSC1 ◁ C2×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 868

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30380, 40);