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2−1+4×C421 #27212270

order13472
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C24×C421 · Schur multiplier (H2) = C25

Aliases

direct product2−1+4×C421

Subgroups

subgroupG/H
center, socleC2×C421C24
commutator, Frattini, cosocleC2C24×C421
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C421 ◁ G

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6736

Conjugacy classes & character table

7157 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#41003013, #41003023, #41003648, …
maximal subgroup of#454×C421, #456×C421, #577×C421, …
maximal normal subgroup of#454×C421, #456×C421, #577×C421, …
maximal quotient of#519×C421, #520×C421, #536×C421, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13472, 50);