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#30777578

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

No aliases for this group.

Splittings

SylowC67 ⋊ #13848

Subgroups

subgroupG/H
centerC23×C4C22×D67
commutatorC23×C67C23×C4
FrattiniC24C23×D67
FittingC2×C4×C4⋊C4×C67C2
socle, prime radical, cosocleC24×C67C24
hypercenterC2×C4×C4⋊C4D67
hypocenterC67#13848
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

1598 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Polycyclic presentation:

2^8,67|a^2=h,b^2=e,c^2=e,d^2=ef,b^a=be,c^a=cf,i^a=i^66,c^b=cg,i^b=i^66,i^c=i^66

Conjugacy classes & character table

2728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 91315);